38 ANALYTICAL MECHANICS 46. Equal Couples. — Two couples are equal when the vectors which represent their torques are equal in magnitude and have the same direction. The three couples in Fig. 30 are equal if G\ = ft = ft- Resultant of two couples is a third couple, whose torque is the vector sum of the torques of the given couples. PROBLEMS. 1. Find the direction and magnitude of the resultant torque of three couples of equal magnitude the forces of which act along the edges of the bases of a right prism. The bases of the prism are equilateral triangles, 2. In the preceding problem let the forces have a magnitude pounds each, the length of the prism be 2 fed, and the* sides of the bases 10 inches. 3. In problem 1 suppose the prism to have hexagonal bases. 4. In problem 2 suppose the prism to be hexagonal. 5. A right circular cone, of weight \V and angle *2 «, i.s plaeed in a circular hole of radius r, cut in a horizontal table. Assuming the coHIi-cient of friction between the cone and the table to be ju, find the leant torque necessary to rotate the former about its axis. 47. Moment of a Force. — The most common method of giving a rigid body a motion of rotation is to put un axle through it and to apply to it a force which acts in a plane perpendicular to the axle. The rotation is produced by the couple formed by the applied force and the reaction of the axle. The torque due to the couple equals the product of Fw. 31. the applied force by the shortest distance from the axle to the line of action of the force. It is of (on- more coin